Adaptive television ghost cancellation system including filter circuitry with non-integer sample delay

ABSTRACT

A television signal ghost cancellation system is described in which a microprocessor is used to develop a mathematical model of the transmission channel which produced a ghosted video signal. The microprocessor determines the coefficient values and delay values for a digital IIR filter from this model. The system uses the IIR filter to cancel ghost signals from the ghosted video signal. The IIR filter includes circuitry for interpolating between successively delayed sample values to cancel ghost signals which are delayed by a non-integer number of sample periods.

This invention relates to a television ghost signal cancellation system which first develops a channel model that, in response to a ghost-free input signal, would produce the ghosted signal Then, based on this model, the system develops a ghost cancellation filter to substantially remove the ghost signal components from the ghosted signal.

Television reception has long been plagued by multipath distortion, the reception of undesired multiple signals. These undesired signals, reflected from buildings and other large objects or resulting from poorly terminated cable networks, appear as delayed versions of the direct television signal, and are commonly referred to as ghost signals in the reproduced image.

The ghost signals are delayed from the direct signal as a function of the relationship of the signal path lengths between the direct and the ghost signals. The randomness of this relationship from one receiver location to another dictates that the phase of the ghost carrier signal may have any relationship to the phase of the direct signal. In order to fully remove the ghost signal from the direct signal, it is necessary to consider the amplitude of the ghost signal, its delay and its carrier phase relative to that of the direct television signal.

To understand the importance of the relative phase of a ghost signal, it is helpful to know more about the television signal itself. Under the NTSC standard, television signals are transmitted in vestigal sideband form. The relatively low frequency components of the baseband signal (from 0-1.25 MHz) are double sideband modulated (DSM) while the higher frequency components (from 1.25 to 4.75 MHz) are single sideband modulated (SSM). The quadrature components of the two sidebands of the DSM portion of the signal are mutually cancelling, so the quadrature component of the DSM video signals is substantially zero. The quadrature components of the SSM portion of the signal, however, are non-zero and may interfere, as a ghost signal, with the in-phase portion of the modulated video signal.

Analytically, the in-phase and quadrature components of the modulated video signal, v(t), may be represented by a complex baseband equivalent defined by the equation (1):

    v(t)=v.sub.I (t)+jv.sub.Q (t)                              (1)

where j is the complex quantity corresponding to the square root of -1 and v_(I) (t) and v_(Q) (t) are the baseband signals which would be obtained if the signal v(t) were synchronously demodulated from, for example, an intermediate frequency (IF) signal, using oscillatory signals that are respectively in-phase with and quadrature phase related to the picture carrier signal. When the signal v(t) is applied to a multipath transmission channel a ghost distorted signal is produced.

FIG. 1 illustrates the importance of the relative phases of the direct and ghost signals. When, for example, the direct signal is a 2T pulse, represented by waveform 10, the ghost signal may be represented by the waveforms 10, 12, 14 or 16 if the relative phase angle between the direct carrier signal and the ghost carrier signal is 0°, 90°, 180° or -90° (270°) respectively. Furthermore, since the relationship between the direct and ghost signal paths is random, any intermediate waveform is also a possibility.

The relative amplitude and phase information of the direct and ghost signals can be determined by demodulating the television signal into in-phase (I) and quadrature (Q) components. The I component being in-phase with the picture carrier of the television signal and the Q component being in-phase with a signal that is phase shifted by 90° relative to the picture carrier. These components describe the television signal in the complex plane where the I and Q components correspond to coordinates along the real and imaginary axes respectively. The convention of referring to the in-phase and quadrature components of the video signals as real and imaginary components respectively is used throughout this application.

As set forth in a paper entitled "Adaptive Multipath Equalization for T.V. Broadcasting", IEEE Transactions on Consumer Electronics, May 1977, pp. 175-181, by H. Thedick, and hereby incorporated by reference, the transmission path which produces a ghost signal may be modeled as a feed-forward system in which the direct signal is reduced in amplitude by an attenuation factor, a, and delayed by an interval of time, τ, to form a ghost signal. The video signal which includes multipath ghost signals may be represented by the equation (2) ##EQU1## where a_(i), is the complex coefficient, and τ_(i) is the relative time delay of the ith signal path. The term n(t) in this equation is the received noise. Including the direct path, there are a total of K paths (i.e. K-1 ghost signals). The magnitude and phase of the complex coefficient a_(i) are the relative attenuation factor and the carrier phase of the ith path, respectively. Let i=1 be the direct path. Ideally, when there is no multi-path problem, a₁ =1, τ₁ =0, and a_(i) =0 for i=2, . . . K.

The ghosted signal represented by the equation (2) is merely a weighted sum of various delayed-versions of the original signal plus noise. In a receiver with no deghosting mechanism, either the real part or the magnitude of r(t) is decoded. This can then yield overlayed images or ghosts on a TV display.

Ghost cancellation systems have been proposed which operate on the in-phase and quadrature components of a video signal. An example of such a system may be found in U.S. Pat. No. 4,703,357 entitled "Adaptive Television Deghosting System", which is hereby incorporated by reference. The system described in that patent uses a digital IIR filter having complex filter coefficients to adaptively remove ghost signals from a received video signal. The IIR filter is conditioned by a control signal first to act as a correlator to determine the time delay of the ghost signals, relative to the direct signal, and then to act as a ghost cancellation filter. Delay values determined by the correlator are preset into variable delay elements which form the taps of the IIR filter, and the tap coefficients are set to predetermined values. The ghost cancellation system then monitors the filtered video signal during a training interval and changes the coefficient values in a sense to minimize ghost signals at the output of the filter in a training interval.

The system described in the above-referenced patent is a digital system which includes an analog-to-digital converter (ADC) that samples the ghosted video signal at a fixed sampling frequency. Consequently, the signals processed by the ghost cancellation filter are valid only at the discrete sampling points. This may present a problem when a ghost signal is delayed with respect to the main signal by an amount of time which is not an integral multiple of the sampling interval. In this instance, the ghost signal which is canceled by the filter may not be the same as the one that contaminates the received video signal and, consequently, a significant artifact of the ghost signal may remain in the processed video signal.

It would be advantageous if a digital ghost cancellation system could be provided which used a simpler IIR filter and which was capable of correcting ghost signals having time delays that are not integral multiples of the sampling interval.

SUMMARY OF THE INVENTION

The present invention is embodied in a ghost cancellation system which includes a control processor that analyzes a received ghosted video signal during a training interval and formulates a channel model describing the transmission channel which produced the ghosted video signal. The control processor then converts this channel model into a set of coefficient values for a complex IIR filter. In one embodiment of the invention, the set of coefficient values produced by the data processor conditions the IIR filter to interpolate delayed samples from among a plurality of time sequential samples to effectively cancel a ghost signal having a relative time delay which is not an integral multiple of the sampling interval. In a second embodiment of the invention, the filter includes sample value interpolation circuitry coupled to at least one tap of the IIR filter to effectively cancel a ghost signal having a relative time delay which is not an integral multiple of the sampling interval.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, referred to above, is a waveform diagram of arbitrary ghost signals relative to a direct signal which is useful for explaining the environment in which the present invention operates.

FIG. 2 is a block diagram of the signal processing portion of a television receiver which includes an embodiment of the present invention.

FIGS. 3 and 4 are waveform diagrams of amplitude versus time showing signals that are useful in explaining the operation of the circuitry shown in FIG. 2.

FIG. 5 is a flow chart that is useful in explaining the operation of the microprocessor shown in FIG. 2.

FIG. 6 is a block diagram of a deghosting filter suitable for use in the circuitry shown in FIG. 2.

FIG. 7 is a block diagram of a complex multiplier suitable for use in the deghosting filter shown in FIG. 6.

FIG. 8 is a block diagram of a portion of the deghosting filter shown in FIG. 6 which illustrates an alternate embodiment of the invention.

FIG. 9 is a block diagram of an interpolator circuit suitable for use in the alternative embodiment of the invention shown in FIG. 8.

FIG. 10 is a table of values which illustrates the programming of the ROM shown in FIG. 9.

As set forth in the above referenced paper by H. Thedick, the transmission channel which adds multipath distortion to a television signal may be modeled as a finite impulse response (FIR) filter. As further stated in the Thedick article, the ghost signals introduced by this transmission channel may be effectively canceled by an infinite impulse response (IIR) filter having a transfer function which is the inverse of the transfer function of the transmission channel.

In the embodiments of the invention described below, a complex IIR filter having adjustable delay values and adjustable coefficient values is used as a ghost cancellation filter. The values for the time delays and coefficient values are determined by a microprocessor from a training signal which is transmitted with the NTSC television signal. These values are determined by analyzing the ghost-contaminated signal prior to any ghost cancellation operations. The delay values and coefficients are then applied to the IIR filter to condition it to cancel ghost signals from the received video signals.

The following is a brief description of the ghost cancellation system shown in FIG. 2. This is followed, in turn, by a more detailed description of the method by which the delay and coefficient values for the ghost cancellation filter are determined and then by a more detailed description of the ghost cancellation filter itself.

In the drawings, broad arrows represent busses conveying multiple-bit parallel digital signals and line arrows represent connections conveying analog signals or single-bit digital signals. Depending on the processing speed of the devices, compensating delays may be required in certain of the signal paths. One skilled in the art of digital signal processing circuit design will know where such delays are needed in a particular system.

Referring to FIG. 2, the signal processing section of a television receiver is shown. Radio frequency (RF) signals are received by an antenna 208 and applied to tuner and IF circuitry 210 The circuitry 210 may, for example, include a conventional television tuner and intermediate frequency (IF) filter and amplifier. In the present embodiment, the pass-band of the IF filter desirably encompasses the modulated sound signals.

The IF signals developed by the circuitry 210 are applied to a conventional envelope detector 242 which develops a baseband composite video signal CV. Conventional sync separator circuitry 244 is responsive to the signal CV to remove the composite synchronization signal, CS, from the composite video signal. The sync separator circuitry 244 also produces a burst gate signal, BG, which may be used to extract the color synchronizing burst signal components from each horizontal line of video signal.

A detector 246, responsive to the composite synchronization signal, CS, detects the last (sixth) pre-equalization pulse preceding the vertical synchronization pulse interval. The circuitry 246 produces an output pulse signal, VS, which substantially coincides with the sixth pre-equalization pulse of each field of the composite video signal. As set forth below, this pulse may be used to locate a training signal which is used to determine the relative delay, the relative amplitude and the relative phase of the ghost signals with respect to the direct signal.

The signals developed by the tuner and IF circuitry 210 are applied to a first synchronous detector 220, a picture carrier extractor circuit 222 and a second synchronous detector 230. The picture carrier extractor circuit 222 produces a first reference signal aligned in phase and frequency with the picture carrier of the direct video IF signal. This first reference signal is applied to the first synchronous detector 220 and to a 90° phase shifter circuit 224. The phase shifter circuit 224 develops a second reference signal, quadrature phase related to the first reference signal. This second reference signal is applied to the second synchronous detector 230. The synchronous detectors 220 and 230 demodulate the IF signals into respective in-phase and quadrature phase components. The in-phase signals are applied to an analog-to-digital converter (ADC) 232 which is responsive to a system clock signal CK for developing digital signals r_(I). Similarly, the quadrature phase signals are applied to an ADC 234 which, responsive to the clock signal CK, develops digital signals r_(Q). The clock signal CK, which may, for example, have a frequency, 4f_(c), substantially equal to four times the NTSC color subcarrier frequency, f_(c), is developed by the phase-locked loop (PLL) 260 described below.

The signals r_(I) and r_(Q) are applied to a deghosting filter 280 and to a microprocessor 282. As set forth below, the deghosting filter 280 includes a complex sampled data IIR filter. The filter 280, under control of the microprocessor 282, filters the ghost-contaminated signals r_(I) and r_(Q) to produce a signal r_(I) ' which approximates the in-phase component of the direct signal to the substantial exclusion of any ghost signals. The signal r_(I) ' is applied to a digital-to-analog converter (DAC) 286, which produces an analog baseband composite video signal, representing the digital signal r_(I) '.

The analog baseband composite video signal is applied to a conventional burst separator 288 which is responsive to the burst gate signal, BG, provided by the sync separator circuitry 244 for separating the color synchronizing burst components from each horizontal line of the composite video signal. The separated burst signals are applied to the conventional PLL 260 which includes a resonant crystal 261 having, for example, a resonant frequency of approximately 4f_(c). The PLL 260 is controlled by the burst signals to produce the 4f_(c) clock signal, CK.

Composite video signals from the DAC 286 are also applied to a conventional video signal processor 290 and to intercarrier sound IF amplifier and detector circuitry 292. The video signal processor 290 may includes, for example, circuitry to separate the luminance and chrominance signal components from the composite video signal and to process these components to produce red, green and blue primary color signals (R, G, and B respectively) for application to a display device (not shown). The intercarrier sound circuitry 292 may include a resonant tuned circuit for separating the 4.5 MHz sound carrier from the composite video signal, a 4.5 MHz IF amplifier and an FM demodulator for developing an audio signal. The audio signal is applied to an audio signal processor 294 which produces an audio signal for application to a speaker (not shown).

The microprocessor 282 may be any one of a number of the currently available microprocessors which include a direct memory access (DMA) instruction, standard arithmetic instructions and interrupt handling capabilities. The microprocessor 282 is coupled to a random access memory (RAM) 284 and a read only memory (ROM) 285. It is further coupled to receive a signal SEL from tuner and IF circuitry 210, indicating the currently selected channel; to receive the signal VS provided by the sixth equalization pulse detector 246 and to receive the clock signal CK. The microprocessor 282 is coupled to provide various signals to the deghosting filter 280 via the busses AD and DATA as described below.

The deghosting operation begins when the signal SEL indicates that a signal from a new channel has been selected. At this time, the microprocessor 282, responsive to the pulse signal VS, executes a DMA instruction to store 768 of the r_(I) and r_(Q) samples, occurring during the interval following the sixth equalization pulse, into the RAM 284. These 768 samples constitute approximately eighty-five percent of one horizontal line period of the incoming signal. This interval includes at least a few samples preceding the leading edge of the vertical sync pulse, samples representing the leading edge of the vertical sync pulse and samples representing the portion of the vertical sync pulse preceding the first serration. This signal is used as a training signal by the microprocessor 282 to determine the delay values and coefficient values which are to be applied to the deghosting filter 280.

The waveform of the in-phase part of this training signal is shown in FIG. 3. The portion of the signal between the sixth equalization pulse and the leading edge of vertical sync has a duration of 0.46 times the horizontal line period (0.46H) and a nominal amplitude of 0 IRE units. The portion of the signal between the leading edge of vertical sync and the first serration in the vertical sync pulse has a duration of 0.43H and a nominal amplitude of -40 IRE units. It is assumed that, in the absence of noise, any deviation from the amplitude value of -40 IRE units during this part of the signal is the result of a ghost signal that is a delayed, attenuated and possibly phase-shifted version of the leading edge of vertical sync.

This signal is constrained by regulations of the Federal Communications Commission (FCC) to have substantially fixed timing and amplitude characteristics. Since this signal is held to close tolerances by the FCC regulations, a model of the signal may be stored the ROM 285 during the manufacture of the receiver and then used by the microprocessor 282 to compare against the received signal and, so, determine the timing amplitude and phase of ghost signals relative to the direct signal. This model includes both the in-phase and quadrature components of the video signal.

As set forth below, the sampled values of the training signal stored in the ROM 285 may have a much higher effective sampling rate than the received video signal. FIG. 4 is a waveform diagram showing the in-phase, I, and quadrature phase, Q, components of the leading edge of vertical sync. 144 samples describing each of the waveforms shown in FIG. 4 are held in the ROM 285. This yields an effective sampling rate of 64 f_(c). Since the training signal is essentially flat in the region following the leading edge of vertical sync, the remaining samples of the training signal, i.e. those describing the interval between the leading edge of vertical sync and the first serration, may be generated by replicating the last samples of the two waveforms.

As described above, in this embodiment of the invention the microprocessor 282 processes samples taken during the training interval to develop a model transfer function which approximates the transfer function of the transmission channel. Using delay values and coefficient values taken from this model transfer function, the microprocessor 282 programs the IIR deghosting filter 280 to cancel the ghost signals from the received video signals.

In the explanation of the algorithm used to develop the channel model, presented below, extensive use is made of vector notation. In general, a signal is represented by a lower case letter, for example, s(t), a vector containing multiple sample values of a signal is represented by an underlined lower case letter, for example, s, and a matrix of sample values is represented by an upper case letter, for example, S.

The algorithms described below have been implemented in the FORTRAN 77 programming language for execution on a VAX computer manufactured by the Digital Equipment Corporation. A copy of these programs is included as an appendix to the application. These programs include a reference to a subroutine CSVDS which is not included in the appendix. This subroutine performs a singular value decomposition of a matrix which has complex elements. It is available to the general public through the LINPACK library package and is described at pp C122-C129 of the LINPACK users guide by J. J. Dongara which is published by Society for Industrial and Applied Mathematics (SIAM).

These programs also contain a list of the values to be loaded into the ROM 285 representing the in-phase and quadrature components of the leading edge of vertical sync as described above in reference to FIG. 4. These values are used to generate the reference signal matrix and reference signal vectors referenced below. In this embodiment of the invention, object code obtained by compiling programs such as those included in the appendix is stored in the ROM 285 along with the data describing the leading edge of vertical sync.

The first step in the algorithm which develops the transfer function is to obtain samples representing the received training signal. As set forth above, the microprocessor 282 is responsive to the signal VS, generated by the sixth equalization pulse detector 246, to load 768 samples of each of the signals r_(I) (t) and r_(Q) (t), provided by the respective ADC's 232 and 234. The complex vector containing the samples of the signals r_(I) (t) and r_(Q) (t) is r. The complex vector containing the samples of the reference training signal, which is obtained by taking every sixteenth sample of the reference samples stored in the ROM 285, is denoted as s. Thus, the leading edge of vertical sync is represented by nine complex sample values.

The next step in the algorithm is to differentiate the vectors r and s This may be accomplished by subtracting the ith entry from the (i+1)st entry for each entry in the vector or by multiplying each of the vectors r and s by a matrix A, defined by equation (3). ##EQU2##

The resulting differentiated vectors are denoted r' and s', respectively. The next step in the procedure is to correlate r' and s' to develop a vector r'_(m). The entries of this vector are developed according to the equation (4). ##EQU3## where s'* indicates the complex conjugate of s'. The magnitude of the absolute value of r'_(m) [n] is an indication

ghost image of the leading edge of vertical sync exists at sample time n+4. If the magnitude of r'_(m) [n] is greater than a threshold value the microprocessor examines values of r'_(m) adjacent to the value at index n and finds the central value, q, in a group of values which exceed the threshold. The sample index q+4 is used as a preliminary ghost delay value. The threshold value used in this test is a function of the signal to noise ratio (SNR) of the received video signal. Desirably, the threshold value is as low as possible to detect even low level ghost signals but not so low that noise in the input video signal is interpreted as a ghost signal. In the present embodiment of the invention, the threshold value is set to twice the root-mean square (RMS) of the differential noise value. The RMS noise value may be determined, for example, by monitoring the video signal during the vertical blanking interval over several field intervals.

Assuming that there exist a direct signal and K-1 ghost signals in the received video signal, where K is an integer, the estimated delays provided by the algorithm described above may be represented by a vector τ described by equation (5). ##EQU4## where τ_(i) is the delay estimate for the ith path. A ghosted training interval can be synthesized by weighting the reference sync values, obtained from the ROM 285, using these delay values. The synthesized training interval may be represented by the equation (6).

    r=Sa                                                       (6)

Where r is the synthesized observation vector, represented by equation (7), ##EQU5## is the reference signal matrix, represented by equation (8) ##EQU6## and a is the synthesization coefficient vector, represented by equation (9). ##EQU7## A synthesization error vector, e, can be represented by the equation (10)

    e=r-Sa                                                     (10)

Due to system noise, this error cannot be zero. The least square (LS) solution of the equation (10) for a gives a minimum norm of the error vector. This solution can be shown to be:

    a.sub.LS +(S.sub.H S).sup.-1 S.sup.H r                     (11)

where H is the conjugate-transpose operator. The least square error, ε(τ), which is defined as the norm square of the least squared error vector e, is given by equation (12)

    ε(τ)=r.sup.H (I-S(S .sup.H S).sup.-1 S .sup.H)r (12)

where I is an N×N identity matrix.

This least square error - and the least square solution for the vector a_(LS) - are functions of the estimated delay vector, τ. Since the edge detection algorithm described above can only provide rough estimates of the relative delays of the ghost signals, this least square error can be used to indicate the accuracy of the delay estimate, the smaller the error the better the estimate of τ. Thus, we can search in the τ space for minimum least square error. Once the optimal τ is reached, the corresponding reference signal matrix is substituted back into (11) to compute the optimal estimate of the synthesization coefficient vector. Note that, during the search procedure, the entires of τ are not restricted to be integral multiples of the sampling interval.

The oversampled vertical sync signal stored in the ROM 285 is used in the present embodiment of the invention to determine the fractional delay time to be added to each of the τ's which were calculated above. In the algorithm described below, the least square error, ε(τ), is used to determine whether a selected delay value is closer to the actual delay than the previously selected delay value.

The inventors have determined that the equation (12) which defines the least square error may be simplified by a singular value decomposition of the matrix S. Let:

    S=UΛV.sup.H                                         (13)

where S is an N×K matrix as set forth above, U is an N×N unitary matrix, V is a K×K unitary matrix and Λ is an N×K diagonal matrix described in the equation (14). ##EQU8## where the values of λ₁, λ₂ . . . λ_(K) are determined by the singular value decomposition operation.

If U₁ is defined as the left-most K columns in U the equation (12) can be reduced to

    ε(τ)=r.sup.H (I-U.sub.1 U.sub.1.sup.H)r        (15)

The singular value decomposition of a matrix is described in section 2.5 of a book by J. C. Nash entitled "Compact Numerical Methods For Computers: Linear Algebra and Function Minimisation", John Wiley & Sons, 1979, pp. 21-22, which is hereby incorporated by reference.

The algorithm for searching the space for the τ space for the minimum least square error is shown in the flow chart of FIG. 5.

In FIG. 5, τ is the vector defined in equation (5) and ε(τ)is the function defined in equation (15). The algorithm described by the flow chart in FIG. 5 adjusts the value of the ghost delays one at a time. With each adjustment, the least square error is evaluated until a local minimum of this value is encountered.

In step 512, the variable I is set to a value of 1, this variable holds the value of the delay time which is to be adjusted. In step 514, all values of a vector Δτ are set to zero except the Ith entry. This entry is set to the sample time, T_(s) /16, of the reference sample vector stored in the ROM 285 (i.e. 1/(64f_(c))).

In step 516, the function is evaluated using the vector τ and the vector τ+Δτ. This is equivalent to using samples from the reference data that coincide with the sample times in the vector τ and samples from the reference data that coincide with the vector τ+Δτ in the function ε(τ). If the value of the function ε(τ) is less when the ghost delay for the Ith ghost is increased, the steps 518 and 520 continue to increase this ghost delay until a minimum value for the function ε(τ) is reached.

Alternatively, if the value of the function ε(τ) at τ+Δτ is greater than at τ, the steps 522, 524 and 526 decrement the delay for the Ith ghost until a minimum value for the function ε(τ) is reached. When the optimum delay value for the Ith ghost signal has been obtained, step 528 determines if more ghost delays are to be optimized. If I is less than K, I is incremented in step 530 and the next ghost delay value is optimized, otherwise, the algorithm ends at step 532.

Using the procedure described above, one can derive the optimal estimates of the synthesization delay vector and the synthesization coefficient vector. Denoting them as τ_(opt) and a_(opt), respectively, the optimal estimate of the transfer function for the transmission channel, h_(opt) (t) is given by equation (16). ##EQU9## Where the a_(iopt) and τ_(iopt) are the respective ith entries of the vectors a_(opt) and τ_(opt).

As set forth above, once the transfer function of the transmission channel has been determined, a ghost cancellation filter may be designed by inserting the delay and coefficient values of this transfer function into an IIR filter. In the algorithm presented above, the starting time for the vector of ghost delay times, τ, is not fixed. Due to variations in the sixth equalization pulse detector 246, the timing of the samples taken by the microprocessor 282 may vary significantly from field to field. To compensate for this variation, the ghost cancellation system used in this embodiment of the invention sets the delay values in the IIR filter to the relative delay values between the term in the transfer function that has the largest magnitude and all subsequent terms. The term with the largest magnitude corresponds to the leading edge of vertical sync, and, as set forth above, all of the subsequent terms are assumed to correspond to ghosts of the leading edge of vertical sync. In addition to adjusting the delay values of the transfer function h_(opt) (t) to be relative to the leading edge of vertical sync, the microprocessor 282 scales the values of the coefficients of the terms of the transfer function which have delay times greater than or equal to that of the leading edge of vertical sync by the inverse of the coefficient value for the leading edge of vertical sync. If, for example; the Lth coefficient value corresponds to the leading edge of vertical sync, the equation (16) would become, ##EQU10##

Since the terms in the transfer function h_(opt) (t) having time delay values less than that of the leading edge of vertical sync may be ignored in synthesizing the ghost cancellation filter, the values of the observed vector, r, corresponding to these terms may also be ignored. The effect of eliminating these values is to reduce the value of N, reducing the computational overhead of the algorithm described above. This reduction in the number of samples may be achieved by locating the leading edge of vertical sync in the observed vector r and eliminating samples which precede it by more than, for example, ten sample periods. This may be done prior to any of the matrix operations set forth above.

When the time delay values of the terms of the transfer function h'_(opt) (t) occur at integral multiples of the sampling period, there is a one-to-one correspondence between the taps of the IIR filter and the terms of the transfer function h'_(opt) (t).

The deghosting filter 280 used in this embodiment of the invention is shown in FIG. 6. In the deghosting filter, the in-phase, r_(I), and quadrature phase, r_(Q), components of the received video signal are applied to the signal input ports of a complex multiplier 610. The real and imaginary parts of the inverse of the complex coefficient a_(Lopt) are applied to the coefficient input ports of the complex multiplier 610 by the microprocessor 282 via the address bus, AD, and data bus, DATA. In the present embodiment of the invention, the microprocessor 282 stores the values of the filter coefficients into the complex multipliers as if it were storing values into the RAM 284.

FIG. 7 is a block diagram of a complex multiplier suitable for use in the present embodiment of the invention. In FIG. 7, the bus DATA is coupled to the respective input ports of two eight-bit parallel input, parallel-output registers 704 and 706. The address bus, AD, is coupled to the input port of a decoding circuit 702. The circuit 702 is responsive to one predetermined value, applied via the bus AD, to pulse a load input signal for the register 704 and responsive to another predetermined value to pulse a different load input signal for the register 706. When the microprocessor 282 loads a coefficient value into one of the complex multipliers used in the deghosting filter 280, it simultaneously applies the real part of the coefficient, via the bus DATA and, the address value which pulses the load signal for the register 704, via the bus AD. Next, the microprocessor applies the imaginary part of the coefficient value via the bus DATA and, the address value which pulses the load signal for the register 706, via the bus AD.

The in-phase and quadrature components of the video signal, I₁ and Q₁, respectively, are multiplied by the in-phase and quadrature coefficient values, I₂ and Q₂, respectively, by the circuitry which includes the multipliers 710, 712, 716 and 718; the subtracter 714 and the adder 720. The multiplier 710 forms the product of the signal I₁ and the coefficient value I₂ and applies the result to the subtracter 714. The subtracter 714 subtracts the product of the signal Q₁ and the coefficient Q₂, provided by the multiplier 712, from the product provided by the multiplier 710 to produce the in-phase output value, I₃. The multiplier 716 forms the product of the signal Q₁ and the coefficient value I₂ and applies this product to one input port of the adder 720. The multiplier 718 multiplies the signal I₁ by the coefficient value Q₂ to generate a second input signal to the adder 720. The output signal provided by the adder 720 is the quadrature signal Q₃.

The multiplication operation performed by the multiplier 610 corresponds to the denominator of the each term of the summation in equation (17) (i.e. 1/a_(Lopt)). This may be considered to be a proportioning of the direct component of the video signal since this coefficient corresponds to the leading edge of vertical sync.

Referring to FIG. 6, the in-phase and quadrature signals provided by the multiplier 610 are applied to respective minuend input ports of subtracters 618 and 620, respectively. The subtracters input ports of the subtracters 618 and 620 are coupled to receive ghost correction signals from adders 666 and 668, respectively. The output signals provided by the subtracters 618 and 620 are the corrected in-phase and quadrature signals, r_(I) ' and r_(Q) ', respectively. As set forth above, in reference to FIG. 2, the signal r_(I) ' is the output signal of the deghosting filter 280.

To simplify the explanation of the ghost cancellation system, the deghosting filter 280 is, for the purpose of this initial description, restricted to having only three taps. As set forth below, it may be desirable for the filter to have a larger number of taps. A filter of this type may be readily designed by one skilled in the art of digital signal processing circuit design as a straightforward extension of the filter shown in FIG. 6.

A programmable three tap delay line 622 provides the three delayed signals for the IIR deghosting filter. The delay line 622 includes two groups of N serially connected delay elements. Each of these delay elements is coupled to the sampling clock signal, CK, and provides a time delay of approximately 70 ns (1/(4 f_(c))). The first group of delay elements--of which the first two, 624 and 626 and the last one, 628, are shown--delay the in-phase component of the video signal. The quadrature component of the video signal is delayed by a second group of delay elements of which the first two, 630 and 632, and the last one, 634 are shown.

The output ports of corresponding delay elements in the in-phase and quadrature delay chains are connected to common switch elements in a crossbar switching matrix. For example, the output ports of the delay elements 624 and 630 are coupled to the switch element 636 and, through the switch element 636, to the switch elements 638 and 640. In the same manner, the output ports of the delay elements 626 and 632 are coupled to the switch elements 642, 644 and 646 and the output ports of the delay elements 628 and 634 are coupled to the switch elements 648, 650 and 652. Each of these three sets of switch elements define a column in the crossbar switching matrix. The switches in each row of the matrix are coupled to each other and to a respectively different complex coefficient multiplier. The switches 636, 642 and 648 are coupled to the multiplier 656; the switches 638, 644 and 650 are coupled to the multiplier 658; and the switches 640, 646 and 652 are coupled to the multiplier 660. The complex multipliers 656, 658 and 660 are identical to the complex multiplier 610 described above in reference to FIG. 7.

Each of the switch elements in the matrix is responsive to a row select signal (RS1, RS2 or RS3) and a column select signal (CS1, CS2 or CS3) provided by switch selection logic 654 to couple the output signals provided by a selected pair of delay elements to a multiplier. In this embodiment of the invention, only one switch in any row and one switch in any column is energized at any given time. The switch selection logic 654 is controlled by values provided by the microprocessor 282 via the busses AD and DAT. The value provided by the bus AD indicates which of three possible row/column selection values is being applied by the microprocessor 282 via the bus DAT. These values are stored internally by the switch selection logic and used to activate the indicated switch elements which provide the delayed signals to the respective multipliers. A programmable tapped delay line of this type is described in U.S. Pat. No. 4,727,424 entitled "Sampled Data Filtering System, Including A Crossbar Switch Matrix, As For A Ghost Cancellation System", which is hereby incorporated by reference.

As set forth above, in this embodiment of the invention, the delay values in the equation (17) are assumed to be in terms of integral numbers of sampling intervals. Consequently, each term in the summation of equation (17), except the first, corresponds to one tap on the in-phase and quadrature delay lines and to one of the coefficient multipliers 656, 658 and 660. Accordingly, the microprocessor 282 applies, via the busses AD and DATA, the in-phase (real) and quadrature (imaginary) components of respectively different ones of the coefficients of the equation (17) to each of the multipliers 656, 658 and 660.

The in-phase signals provided by the multipliers 658 and 660 are summed in an adder 662. The combined signal provided by this adder is, in turn, summed with the in-phase signal provided by the multiplier 656 in the adder 666. As set forth above, the signal provided by the adder 666 is the in-phase component of the ghost correction signal that is applied to the subtracter 618.

The quadrature signals provided by the m' multipliers 658 and 660 are summed by an adder 664 and the resultant sum is applied to the adder 668. The adder 668 adds this value to the quadrature signal provided by the multiplier 656 to develop the quadrature component of the ghost cancellation signal which is applied to the subtracter 620. As set forth in the Thedick reference, an IIR filter such as that shown in FIG. 6 will effectively cancel multipath distortion in a video signal when there is one tap of the delay line and one coefficient multiplier for each ghost signal component of the received video signal.

To simplify the explanation of the entire ghost cancellation system, it was assumed above, that each ghost signal is delayed with respect to the direct signal by an amount of time that is an integral multiple of the sampling interval. When this is not true, that is, when a ghost signal is delayed by an amount of time which is not an integral multiple of the sampling interval, modifications may be desirable to the system described above to achieve effective ghost signal cancellation. In general, an IIR filter may be modified to cancel ghost signals having delay times interstitial to two successive delay times which may be obtained from a tapped delay line, if an interstitially delayed signal is interpolated from the available delayed signals-and used as a tap of the IIR filter. Two methods of interpolation are presented below. The first method involves a straightforward extension of the structure shown in FIG. 6 which adds more rows of switch elements to the crossbar matrix and more complex multipliers. In addition, the microprocessor 282 is programmed to calculate additional coefficient values for taps surrounding the fractional sample delay. The second method inserts an interpolator circuit at each output port of the variable delay line. This interpolator is responsive to a signal produced by the microprocessor 282 to provide in-phase and quadrature signals having effectively the same delay as the ghost signal.

The following is an explanation of the calculations which constitute the algorithm to derive the additional coefficients values for the first method described above. For all ghost delays, τ_(i), let:

    k.sub.i =INT(τ.sub.i /T.sub.s) (18)

where T_(s) is the sampling interval (1/4f_(c)) and INT(x) gives the largest integer that is not greater than x. Furthermore, let P_(ij) represent one delay value in a group of delay values, which includes k_(i), and which correspond to possible delay line taps surrounding the ith ghost signal delay. In the algorithm described below, the ith ghost cancellation signal is interpolated from J_(i) successive taps of the delay line. To differentiate the coefficient values in the present algorithm from those used in the algorithm to derive the equivalent channel response, the present coefficient values are denoted as b_(ij). Moreover, to simplify the complex matrix equations used in this algorithm, the value L in equation (17) is assumed to be equal to one and the leading edge of vertical sync is assumed to occur at τ₁ =0.

When the assumptions set forth above are substituted into the equation (17), an equation (19) is obtained. ##EQU11## In this equation, the optimal values of the coefficients, b_(ij), are unknown.

As set forth above, the observed vector r may be closely approximated according to the equation (20).

    r≈r.sub.opt =S.sub.opt a.sup.T.sub.opt             (20)

where S_(opt) is the reference signal matrix described by equation (8) where τ=τ_(opt).

For the present algorithm, only the last row of the reference signal matrix, the vector S-_(opt) T.sub.(N), need be considered. Under this constraint, the equation (20) becomes:

    r.sub.opt [N]=s.sub.opt [N].sup.T a.sub.opt                (21)

where ##EQU12## From the transfer function defined by equation (19), an equation (23) similar to the equation (21) can be derived.

    y[N]=s[N].sup.T b                                          (23)

where y[N] is an approximation of r[N] and s[N] is a reference signal vector defined by equation (24), ##EQU13## and the coefficient vector b is defined by the equation (25). ##EQU14## The inventors have determined that the coefficient values b may be determined by obtaining the minimum mean square error between r_(opt) [N] and y[N] when the p_(ij) 's are selected in advance. This solution is represented by the equation (26).

    b.sub.MMSE ={E(s*s.sup.T)}.sup.-1 {E(s*s.sup.T.sub.opt)    (26)

Where * represents the conjugate operator, T represents the transpose operator and E() represents the expectation operator when the vectors are treated as random vectors. The time index N is dropped since the processes are stationary. In this embodiment of the invention the term E(s*s^(T)) is equivalent to the covariance matrix between s* and s^(T) and E(s*s^(T)) is equivalent to the cross-covariance s matrix between s* and s^(T) _(opt). In the calculations which evaluate the equation (26), the vectors s and s_(opt) are transformed to be zero-mean vectors and are assumed to have a flat spectral density within the video frequency range. A discussion of random variables and their properties including a discussion of the covariance matrix may be found in chapters 9 and 10 of a book by G. R. Cooper and C. D. McGillem entitled Methods of Signal and System Analysis; Holt, Rinehart, Winston, 1967, which is hereby incorporated by reference.

The coefficient vector b_(MMSE) determined by this method may be used to set the coefficient values for the IIR filter where the delay values are determined by the defined by the equation (27). ##EQU15## The inventors have determined that, when the ghost time, τ_(i), is substantially equal to k_(i) T_(s), that J_(i) may be set to a value of one. When, however, there is a significant difference between τ_(i) and k_(i) T_(s), setting J_(i) to a value of four produces more satisfactory results. Using this scheme, two samples before and two samples after the fractional ghost delay are interpolated to obtain an equivalent sample having the fractional ghost delay.

The algorithm set forth above is implemented in a computer program, written in the FORTRAN 77 computer language. This program is included in the appendix of the present application

An alternative to the interpolation scheme described above is to insert sample value interpolation circuitry between the output ports of the programmable delay line 622 and the signal input ports of the coefficient multipliers, 656, 658 and 660, as shown in FIG. 8. Each of interpolators, 810, 812 and 814, shown in FIG. 8, includes two compensated linear interpolators which may be, for example, of the type shown in FIG. 9. The compensated interpolator shown in FIG. 9 includes a linear interpolator, 920, which averages the values of successive samples according to a proportioning factor F, to produce an interpolated sample value. By averaging the samples, the interpolator performs the function of a low-pass filter. This filtering of the video samples may produce undesirable phase and amplitude errors in the interpolated signal To compensate for these errors, the interpolator shown in FIG. 9 includes a compensation filter, 950. The amount of compensation provided to the interpolated signal depends on the value of the proportioning factor F.

Referring to FIG. 8, in this embodiment of the invention, the proportioning factors are applied to the interpolators 810, 812 and 814 by the microprocessor 282. Both of the interpolation circuits in an interpolator are provided with the same factor value, F. The value of F applied to each of the interpolators 810, 812 and 814 may be different, however, since this value is the fractional part of the delay value τ_(i) associated with the ith ghost signal (i.e. τ_(i) =τ_(iopt) -τ_(Lopt)). The value F is applied to the input port of a register 932 of the interpolator circuit via the bus DATA while a value applied, via the bus AD, to a decoder 330 conditions the decoder to pulse the register 932, causing it to load the value applied to its input port. The value in the register 932 is applied to the address input port of a ROM 934 which provides a value (1-F) to the linear interpolator 920 and provides a value C to a multiplier 936. The value of C determines the magnitude of the compensation signal which is added to the interpolated signal by an adder 960.

FIG. 10 is a table which illustrates the programming of the ROM 934 for an interpolator circuit having a granularity of (1/8)T_(s).

The interpolation circuitry shown in FIG. 9 is described in detail in U.S. Pat. No. 4,694,414 entitled "Digital Delay Interpolation Filter With Amplitude And Phase Compensation", which is hereby incorporated by reference.

In the context of the algorithm presented above for developing a ghost cancellation filter from a calculated transfer function of the transmission channel, this interpolation circuitry is used as follows. When the microprocessor 282 applies the delay values from the equation (17) to the programmable delay line 622 of the deghosting filter 280, it apportions the delay values between the delay line 622 and a selected one of the interpolators 810, 812 or 814. The amount of the delay value, τ_(i), which is realized by the programmable delay 622 is substantially equal to the integer part of the quantity τ_(i) /T_(s) minus 1, times T_(s). The remainder of the delay value, T_(s) plus the fractional part of T_(s), is realized in the selected interpolator by applying the fractional part of the value τ_(i) as the proportioning factor F. The extra sample period of delay is inherent to the selected interpolator, as set forth in the TOTAL-DELAY column of the table in FIG. 10.

To compensate for the effects of system noise on the deghosting system presented above, it is contemplated that several estimates of the transmission channel (i.e. equation 17) may be made over several video field intervals and that the coefficient and delay values from these estimates may be averaged to obtain the final coefficient and delay values for use by the deghosting filter 280.

While the ghost cancellation system described above is a digital system which removes multipath distortion from video signals, it is contemplated that the invention may also be implemented using analog components and used to remove multipath distortion from other types of signals. ##SPC1## 

What is claimed is:
 1. A system for eliminating ghost signals from a TV signal, comprising:first means for providing first and second sampled data signals occurring at a predetermined frequency, said first and second sampled data signals representing in-phase and quadrature phase components of said TV signal, said TV signal including a training signal component and subject to including multipath ghost components; second means for providing first and second reference signals respectively representing in-phase and quadrature phase components of said training signal component free of any ghost components; control means coupled to said first and second means and responsive to said first and second reference signals and said first and second sampled data signals, for detecting the occurrence of said multipaths ghost components with temporal resolution less than the period of said sampled data signals and generating delay control signals representing temporal relationships between said training signal and said multipath of ghost component signals, and for generating coefficient control signals related to intensity values of said multipath ghost component signals; and filter means including:signal combining means having a first input port coupled to said first means, having a second input port and an output port; a cascade connection of signal scaling means and signal delaying means coupled between said second input port and said output port of said signal combining means, said signal scaling means having a control input port for receiving coefficient control signals and responsive thereto for scaling signals, said signal delay means including means for effectively delaying samples by non-integer periods of said samples and responsive to said delay control signals for programmably delaying samples.
 2. A system for correcting multipath distortion, comprising:a source of input signal including a direct signal having a training signal component, and further including delayed signals which constitute undesirable multipath distortion components; a source of reference signal representing said training signal substantially free of any multipath distortion; infinite impulse response filtering means having programmable tap delays, an output port, an input port coupled to said source of input signals and having programmable filter coefficient values; control means coupled to said source of input signal and to said source of reference signal for developing a mathematical model of a signal filtering system which, responsive to said reference signal produces a signal substantially representing said input signal, and for programming the coefficient values of said infinite impulse response filtering means with coefficient values determined from said mathematical model and including means for programming the tap delays of said infinite impulse response filtering means with delay values determined from said mathematical model to condition said infinite impulse response filtering means to provide, as an output signal at said output port, said direct signal to the substantial exclusion of said delayed signals.
 3. The system set forth in claim 2 further comprising:a source of sampling clock signal for providing clock pulses at a predetermined frequency; analog-to-digital conversion means, coupled to said source of input signal for developing digital samples representing said input signal at instants determined by said sampling clock signal, said analog-to-digital conversion means being coupled to provide said digital samples to said infinite pulse response filtering means and to said control means; and wherein said source of reference signal includes read-only memory means programmed with sample values representing said reference signal; and said control means includes:read-write memory means; and data processing means coupled to said read-only memory means and to said read-write memory means, and being controlled by a program to store a plurality of said digital samples representing the training signal component of said input signal into said read-write memory means, to generate said mathematical model of said signal filtering system and to generate said coefficient values and said tap delay values for said infinite impulse response filtering means.
 4. The system set forth in claim 3 wherein:said infinite impulse response filtering means includes:an input port for applying the digital samples representing said input signal; first signal combining means, coupled to said input port for combining the digital samples representing said input signal with digital samples representing a correction signal to produce said output signal; programmable signal delaying means, coupled to said first combining means, for delaying the signal provided thereby, having a plurality of output ports and having circuitry for providing delayed versions of the signal provided by said combining means at each of said output ports, wherein the amount of time delay imparted to the signal provided at each of said output ports is determined by first programming control signals; a plurality of programmable coefficient multiplying means, each coupled to a respectively different one of the output ports of said programmable signal delaying means for multiplying the signals provided thereby by respectively different ones of said coefficient values, each of said coefficient values being determined by second programming control signals applied to each of said plurality of programmable coefficient multiplying means; and second signal combining means coupled to each of said plurality of programmable coefficient multiplying means for combining the respective signals provided thereby to generate said correction signal; and said data processing means is controlled by said program to generate said first programming control signals and said second programming control signals.
 5. The system set forth in claim 4 wherein said programmable signal delaying means includes:sampled data signal delaying means, coupled to said source of sampling clock signal, having an input port coupled to receive the output signal of said first combining means and responsive to said second programming control signals for providing a plurality of selected delayed versions of the output signal of said first combining means at respective output ports, each of said selected delayed versions of said output signal of said first combining means being delayed with respect to the output signal of said first combining means by respectively different integer multiples of the period of said sampling clock signal; and signal interpolation means, coupled to at least one of the output ports of said sampled data signal delaying means and responsive to said second control signals for effectively delaying the signal provided at the one output port of said sampled data signal delaying means by an amount of time substantially equal to N/M times the period of said sampling clock signal where M is an integer greater than 1 and N is a positive integer having a value determined by said second control signals
 6. A system for correcting multipath distortion in a video signal, comprising:a source of video signal including a direct signal having a training signal component, said direct signal modulating a carrier signal, and further including delayed signals which constitute undesirable multipath distortion components; demodulation means, coupled to said source of video signal, for demodulating said video signal into first and second signal components representing baseband signals that are respectively in-phase with and quadrature phase related to said carrier signal; complex infinite impulse response filtering means having first and second input ports coupled to receive said first and second signals, respectively, and having programmable complex filter coefficient values and programmable tap delays; a source of first and second reference signals representing, respectively, the training signal components of said first and second signals to the substantial exclusion of any multipath distortion components; control means coupled to said demodulation means and to said source of first and second reference signals for developing a mathematical model of a signal filtering system which, responsive to said first and second reference signals produces first and second synthesized signals that substantially represent the training signal components of said first and second signals, respectively, and for programming the complex coefficient values of said infinite impulse response filtering means with complex coefficient values and said programmable tap delays with delay values determined from said mathematical model, to condition said infinite impulse response filtering means to provide, as an output signal at said output port, the first signal component of said direct signal to the substantial exclusion of said delayed signals.
 7. The system set forth in claim 6, further comprising:a source of sampling clock signal for providing clock pulses at a predetermined frequency; first and second analog-to-digital conversion means, coupled to said demodulation means for developing, respectively, first and second sequences of digital samples representing said first and second signals at instants determined by said sampling clock signal, said first and second analog-to-digital conversion means being coupled to provide said first and second sequences of digital samples to said infinite impulse response filtering means and to said control means; and wherein said source of said first and second reference signals includes read-only memory means programmed with sample values representing said first and second reference signals; and said control means includes:read-write memory means; and data processing means coupled to said read-only memory means and to said read-write memory means and being controlled by a program to store a plurality of digital samples from each of said first and second sequences of digital samples, representing the training signal component of said video signal, into said read-write memory means, to generate said mathematical model of said signal filtering system and to generate said complex coefficient values and said tap delay values for said infinite impulse response filtering means.
 8. The system set forth in claim 7 wherein:said infinite impulse response filtering means includes: first and second input ports for applying said first and second sequences of digital samples; first and second signal combining means, coupled respectively to said first and second input ports for combining said first and second sequences of digital samples with respective first and second further sequences of digital samples representing respective first and second correction signals to produce first and second sequences of corrected samples, respectively, wherein said first sequence of corrected samples is the output signal of said infinite impulse response filtering means; programmable signal delaying means, coupled to said first and second combining means for delaying the respective first and second sequences of corrected samples provided thereby, having a plurality of output ports and having circuitry for providing delayed versions of said first and second sequences of corrected samples at each of said output ports, wherein the amount of time delay imparted to the delayed versions of said first and second sequences of corrected samples provided at each of said output ports is determined by first programming control signals; a plurality of programmable complex coefficient multiplying means each coupled to a respectively different one of the output ports of said programmable signal delaying means for multiplying the delayed versions of the first and second sequences of corrected samples provided thereby by respectively different ones of said complex coefficient values to develop first and second sequences of scaled sample values, each of said complex coefficient values being determined by second programming control signals applied to each of said plurality of programmable complex coefficient multiplying means; andthird and fourth sample combining means, coupled to each of said complex coefficient multiplying means for combining the respective first and second sequences of scaled sample values provided thereby to generate said first and second sequences of corrected samples, respectively; and said data processing means controlled by said program to generate said first programming control signals and said second programming control signals.
 9. The system set forth in claim 8 wherein said programmable signal delaying means includes:sampled data signal delaying means, coupled to said source of sampling clock signal, having first and second input ports coupled to receive the first and second sequences of corrected samples, respectively, and responsive to said second programming control signals for providing a plurality of selected delayed versions of said first and second sequences of corrected samples at respective output ports, each of said selected delayed versions of said first and second sequences of corrected samples being delayed with respect to said first and second sequences of corrected samples by respectively different integer multiples of the period of said sampling clock signal; and sample value interpolation means, coupled to at least one of the output ports of said sampled data signal delaying means and responsive to said second control signals for effectively delaying the selected delayed version of said first and second sequences of corrected samples provided thereby by an amount of time substantially equal to N/M times the period of said sampling clock signal where M is an integer greater than 1 and N is a positive integer having a value determined by said second control signals.
 10. A system for correcting distortion in a sampled data signal comprising:a source of sampled data input signal including a training signal component, said input signal subject to being distorted, and samples of said input signal occurring at a predetermined regular rate; a source of reference signal representing said training signal substantially free of said distortion; filter means including signal combining means having a first input port coupled to said source of sampled data input signal, a second input port and an output port, means coupled between said output port and said second input port of said combining means, and having control input ports, for providing scaled and delayed samples responsive to coefficient and delay control signals applied to said control input ports, said means for providing scaled and delayed samples including means to effectively delay samples by non-integer sample periods; control means coupled to said source of sampled data input signal and said source of reference signal for generating said coefficient and delay control signals, including means for generating coefficient and delay values to synthesize a signal substantially representing said training signal component and generating said coefficient and delay control signals from said coefficient and delay values. 